Aims:The non-conservative gravitational potential of barred galaxies, or of any other non-axisymmetric structure, produces a loss of energy in infalling particles of the intergalactic medium into the galaxy, which are trapped in its potential. This dynamical friction can contribute towards increasing the total mass of barred galaxies. Methods: Analytical calculations of the energy loss are carried out using the orbits of the particles derived numerically. Theoretical predictions are compared with observations through the statistical analysis of the rotation curves of barred and non-barred galaxies, either in cluster or field galaxies. Results: There is a net effect of accretion, but it is normally very low in relative terms. It is only significant (>10% of the total mass of the dark matter halo in the life of the galaxy) if the density of the intergalactic medium is higher than ~3× 1013~M_&sun; /Mpc3 (or considerably lower in cases of motions of the galaxies close to the IGM average motion, or perpendicular to the plane of the galaxy, or when the halo mass is low). Data on rotation curves do not show clear trends towards higher halo mass for barred galaxies, only slight trends for early-type spiral galaxies. In any case, the statistical uncertainties are limited to the detection of differences in masses >≈20%, so the effect of bar-driven injection of intergalactic matter into galactic halos might be present with relative contributions to the average mass of these barred galaxies lower than 20%.